The vow that began with the words "If God will ... clothes to wear" in verse 20 continues here. Jacob is speaking to God in the third person. This can be stated in the second person. "If you will ... clothes to wear ... then you, Yahweh, will be the God that I will worship" (See: [[rc://en/ta/man/translate/figs-123person]])
Here "house" stands for Jacob's family. Alternate translation: "to my father and the rest of my family" (See: [[rc://en/ta/man/translate/figs-metonymy]])